Direct Rashba spin-orbit interaction in Si and Ge nanowires with different growth directions

A strong and electrically tunable spin-orbit interaction is crucial in modern condensed-matter fields, such as spintronics, topological quantum matter, and spin-based quantum computing. Such a tunable spin-orbit interaction of novel origin and high strength was recently discovered for holes in Ge/Si core/shell nanowires Phys. Rev. B 84, 195314 (2011). Here, the authors consider Si and Ge nanowires of rectangular cross section. The hole spectra are calculated and their parameter dependences analyzed, including growth directions, dimensions, strain, and electric and magnetic fields. Unusually large Rashba spin-orbit energies (meV) are found not only for Ge but also for Si nanowires, provided that their growth direction differs from that of current complementary metal-oxide semiconductor devices.